Normality testing is the assessment of whether process data sufficiently follows a normal distribution for standard capability formulas to remain valid - it is a critical assumption check before using Gaussian-based Cp and Cpk interpretations.

What Is Normality testing?

• Definition: Statistical and graphical evaluation of distribution shape versus normal model assumptions.
• Common Tests: Anderson-Darling, Shapiro-Wilk, and probability-plot diagnostics.
• Typical Violations: Skewness, heavy tails, multimodality, and mixed-population effects.
• Decision Output: Proceed with normal capability, transform data, or switch to non-normal methods.

Why Normality testing Matters

• Model Validity: Using normal formulas on highly skewed data can misstate defect risk dramatically.
• Method Selection: Normality result determines whether transformation or percentile methods are needed.
• Risk Transparency: Assumption checks prevent false confidence in capability dashboards.
• Root-Cause Insight: Non-normality often signals mixed process states or hidden special causes.
• Audit Compliance: Quality systems expect documented distribution assessment before index reporting.

How It Is Used in Practice

• Visual Screening: Inspect histogram and normal probability plot before formal tests.
• Statistical Testing: Run normality tests with awareness that large N can detect tiny, irrelevant deviations.
• Action Path: Apply transformation or non-normal capability method when assumption violation is material.

Normality testing is the prerequisite check for meaningful Gaussian capability analysis - validate the foundation before trusting the index.